Structural behaviour of bent angle-steel joints embedded in transmission tower foundations: full-scale testing and finite element modelling

1 Introduction

Transmission towers are important load-bearing structures in power transmission lines, and their safety is directly related to the stable operation of power systems. The bent angle-steel joint transfers loads between the main tower leg and the concrete foundation. Under vertical loads and auxiliary inclined or horizontal loads, the angle steel member, bolts and gusset plates are subjected to a complex stress state, which may readily lead to local stress concentration. Therefore, investigating the structural behaviour of this type of joint is of practical importance for transmission tower design.

In recent years, extensive full-scale tests and numerical simulations have been conducted on the load-carrying behaviour and failure mechanisms of transmission tower systems. (Tian et al., 2018) investigated transmission-tower failure under combined vertical, transverse and longitudinal equivalent static loads, and showed that member instability and progressive stress redistribution controlled the failure process. (Tian et al., 2020) further carried out a full-scale test and numerical analysis of a latticed steel tubular transmission tower and demonstrated that nonlinear finite element models could capture the main failure sequence of the tower. (Fu et al., 2020) studied the stress state and failure path of a tension tower under multiple service and extreme loading conditions and reported that the critical members and failure path changed with the load combination. (Gao et al., 2022) conducted full-scale tower tests and found that local buckling of highly stressed members and connection effects were important causes of overall failure. (Qu et al., 2020) examined high-strength angle steel members under axial compression and observed that buckling resistance was closely related to slenderness and end restraint. (Bezas et al., 2022) proposed stability design recommendations for steel lattice transmission towers, emphasising the influence of geometric imperfections, member connectivity and global-frame interaction. For angle connections, (Bernatowska and Ślęczka, 2021a; Bernatowska and Ślęczka, 2021b; Bernatowska and Ślęczka, 2022) investigated net-section fracture, block tearing and local failure modes of single-leg-connected angle steel members under tension and reported that bolt-hole weakening, eccentric load transfer and stress concentration made the failure of the connection region more complicated. (Xu et al., 2022) examined angle-steel joints for conductors in lattice transmission towers, and the analytical and finite element results clarified the load transfer and stress distribution of the joint. (Gan et al., 2021) proposed a simplified joint-slippage model for bolted joints in lattice transmission towers and found that bolt slip affected the numerical prediction accuracy. (Xu et al., 2025) investigated angle members with double-shear splice connections and found that the splice detail affected axial stiffness, stress redistribution and compression resistance. (Wang et al., 2023) studied a Q690 steel tubular transmission tower and found that nonlinear finite element analyses could reproduce the observed failure mechanism and identify the highly stressed members. (Wu et al., 2025) investigated Y-shaped retrofitting angle-steel members and reported that the retrofitting configuration improved the axial compression capacity and delayed buckling. (Wu et al., 2024) also studied the behaviour of T-shaped diagonal members and found that retrofitting the member increased the ultimate load-bearing capacity, with failure controlled by member buckling and connection effects. (Zeng et al., 2025) proposed buckling-restraint-reinforced angle-steel members and demonstrated that buckling restraint reduced the member deformation and improved the wind-resistant capacity of transmission towers. (Zhu and Xie, 2025) analysed transmission tower foundations under tensile loading and showed that the numerical connector model could capture the load-transfer path and tensile failure response of the foundation.

However, the structural behaviour of bent angle-steel joints embedded in concrete foundations has not been sufficiently clarified by full-scale tests, especially under combined vertical and auxiliary loads. In this study, full-scale tension and compression tests were conducted on bent angle-steel joint specimens to obtain the load-strain responses, stress development and failure modes. Finite element models were then established to analyse the principal-stress and von Mises stress distributions under the same loading conditions. By comparing the test observations with the numerical results, the critical regions, failure-controlling component and strength margin of the gusset plate were evaluated, providing a reference for the engineering application of this type of joint in transmission tower foundations.

2 Full-scale tests on bent angle-steel joints

2.1 Specimen design

Figure 1a shows the details of the bent angle-steel joint used in the test. The main load-transferring member was made of Grade Q420 angle steel L125 × 10 mm, with a total net cross-sectional area of 4874 mm² for the double-angle member used in the strength check. The upper loading steel plate was 480 × 480 × 20 mm, and the bottom steel plate was 800 × 800 × 40 mm; the remaining construction dimensions, bent region and gusset-plate configuration are shown in Figure 1. Figure 1b shows the cross-section at Section 1-1, where the four faces of the angle-steel joint are numbered as Faces I–IV for strain gauge layout and subsequent stress analysis. The bent angle-steel member had a special geometry. The upper segment connected to the tower leg was inclined, with an inclination angle consistent with the slope of the tower-leg main member, whereas the lower segment connected to the concrete foundation was perpendicular to the ground. Closely-spaced bolt holes were fabricated at the top and bottom ends of the bent angle-steel member, and Grade 8.8 high-strength bolts were used for the connections. This arrangement allowed the joint assembly to be divided into several components during transportation and then assembled on site. A total of 36 strain gauges were arranged on the joint, as shown in Figure 2.

2.2 Loading scheme

Separate tension and compression tests were conducted to simulate the loading state of the bent angle-steel joint embedded in a transmission tower foundation. Hydraulic jacks and a 5000 kN compression testing machine were used for loading, and load cells and strain gauges were used to monitor the applied loads and strain development. The joint transfers the force from the main tower leg together with forces from adjacent members. Accordingly, the load along the main-member direction was taken as the primary load and was increased step by step until failure occurred, whereas the auxiliary loads from adjacent members were applied first and then kept constant. In the tension test, one inclined tensile load was applied along the diagonal-member direction. In the compression test, two horizontal compressive loads were applied in the x- and y-directions. The target values of these auxiliary loads were determined from the internal-force distribution of a prototype tower. The loading increments were 20 kN for the auxiliary loads and 50 kN for the primary load. At each loading stage, the applied loads, strain responses and visible deformation of the joint were recorded. As the displacement was not continuously monitored, the discussion is focused on the load-strain response, stress development and observed failure modes.

2.2.1 Tensile loading scheme

Figure 3 shows a planar schematic of the tensile loading arrangement. The tensile loads were applied along the main-member direction and one diagonal-member direction. Specifically, the inclined tensile load in the diagonal-member direction was first applied and increased to the prescribed target value of 180 kN. This inclined load was then kept constant, and the tensile load along the main-member direction was applied in a stepwise manner. Therefore, the loading directions shown in Figure 3 correspond to the actual member directions in the test plane, rather than to load components decomposed from a single external force. During each loading step, the applied loads, strains and visible deformation of the joint were recorded. Loading was continued until the loss of load-carrying capacity.

2.2.2 Compression loading scheme

The compression test was conducted using a 5000 kN compression testing machine. Figure 4 presents a schematic of the loading arrangement, including the vertical compressive load and two horizontal components in the x- and y-directions. The horizontal compressive loads were first increased to 100 kN in the x-direction and 80 kN in the y-direction, and were then kept constant. A vertical compressive load was subsequently applied along the main-member direction and increased step by step. In this way, the horizontal effects from adjacent members were kept constant, while the vertical load was used to evaluate the compressive response of the joint.

2.3 Test results of the joint in tension

The load-strain behaviour and failure mode of the joint were analysed in this section. Based on the strain-gauge layout, strain gauges C12, C17, C32 and C37 were selected as representatives on the four faces of the angle steel. Among them, C12 was the critical strain gauge at which first yielding occurred under tension, and C17, C32 and C37 were used to reflect the stress development of the angle steel on other faces.

2.3.1 Tensile load-strain curves

Figure 5 shows the tensile load-strain curves of representative gauges on Faces I-IV of the specimen. During the tension test, the strains of the angle steel generally increased as the load increased. Before the vertical tensile load was applied, the 180 kN inclined load produced only limited initial strains, indicating that the joint was still in the elastic stage. After the vertical tensile load was applied, most measured strains increased approximately linearly with the load. However, the strain at C12 on Face I increased more rapidly than those at the other gauges as this region was close to the loaded end and was affected by local stress concentration and eccentric load transfer through the bolted connection. When the vertical tensile load reached 800 kN, the strain at C12 reached 2028 με, corresponding to a calculated local stress of 417.8 MPa and indicating local yielding. After local yielding, the load-strain relationship became nonlinear; sudden changes in individual strain curves were mainly caused by yielding of the local angle-steel region, redistribution of load among adjacent angle legs and bolts, and local deformation of the loading plate. Therefore, C12 was identified as the critical strain gauge under tensile loading.

2.3.2 Failure mode under tension

During the tension test, no obvious deformation was observed in the joint at the initial loading stage, and the strain variations were generally consistent with the applied load. As the vertical tensile load increased, the strain on Face I developed rapidly, and gauge C12 reached the yield strain first. When the inclined tensile load was kept at 180 kN and the vertical tensile load was increased to 1100 kN, the strain at C12 reached 3005 με, the double angles on Face I yielded, and tearing occurred in the top loading steel plate, causing the joint to reach failure. Tearing of steel was located at the auxiliary loaded-end steel plate used in the test, as shown in Figure 6, rather than in the embedded gusset plate itself. Its location was near the upper loaded end of the auxiliary loading plate which is consistent with stress concentration in the loaded-end connection region. No significant deformation or yielding of the gusset plate was observed during testing. The observed damage was concentrated near the loaded end. Yielding first developed in the angle member on Face I, and the final loss of capacity was associated with tearing of the auxiliary loading plate rather than failure of the embedded gusset plate. The region near the loaded end therefore remained a critical region requiring attention in tensile design and test-fixture design.

2.4 Test results of the joint in compression

Based on the strain-gauge layout, strain gauges C17, C32, C37 and C41 were selected as representatives under compressive loading. Among them, C17 exhibited a relatively large strain in the later stage of compression loading and could reflect the stress development in the critical region of the angle steel. C32 and C37 were located in the critical region of the angle steel on Face III and could reflect the transition of the angle steel from elastic response to yielding and bending instability. C41 was used to characterise the strain of the gusset plate and to provide a comparison with the strain gauges on the angle steel.

2.4.1 Analysis of compression load-strain curves

Figure 7 shows the compression load-strain curves of representative gauges on the joint. During compression loading, the strain development differed significantly among the four faces of the angle steel. In the initial loading stage, the strain variation at each point was limited, indicating that the joint as a whole remained in the elastic response stage. As the vertical compressive load increased, the strains at several gauges on the angle steel increased rapidly, and the joint behaviour gradually changed from overall elastic behaviour to local bending with stress redistribution. When the x-direction compressive load reached 100 kN, the y-direction compressive load reached 80 kN and the vertical compressive load reached 1300 kN, visual observations during the test showed that bending started in the angle steel member on Face III. Upon further loading to 1500 kN, the bending deformation of the angle steel on Face III became more significant. When the vertical compressive load reached 1700 kN, the strain at strain gauge C17 reached 1949 με, corresponding to a calculated local stress of 401.5 MPa, close to the yield strength of the steel. Finally, when the vertical compressive load reached 1989 kN, flexural yielding occurred in the angle steel, and the joint attained its load-carrying capacity. The most significant strain development occurred on Face III as defined in Figure 1, and strain gauges C32 and C37 on this face reached the yield strain first. During compression loading, the deformation of the yielded region increased gradually with increasing load, whereas the stress increase in the yielded region was limited. The additional load was mainly carried by the parts of the same face that had not yet yielded, indicating that the joint retained a certain load-carrying capacity after local yielding. The strains at gauges near the gusset plate were relatively small, and no clear signs of yielding were observed. These observations indicate that the gusset plate was not the component controlling compression failure.

2.4.2 Failure mode under compression

The compression failure was characterised by local bending of the angle steel on Face III. The marked region in Figure 8 lies on the compressive side of the angle member close to the bolted connection, which agrees with the larger strain recorded on Face III. No visible damage was found in the gusset plate during the test. As the vertical load increased, deformations became concentrated in the compressed angle leg and the adjacent bolted region. After local yielding, the yielded zone continued to deform, while the surrounding unyielded parts still participated in load transfer. Final failure could therefore be described as flexural yielding of the compressed angle steel rather than gusset-plate failure.

3 Finite element analyses of bent angle-steel joints

3.1 Numerical model

Figure 9 shows the numerical model for the joint. In the model, the angle steel and gusset plates were simulated using solid elements, and the steel components were described by a bilinear isotropic elastic-plastic constitutive model. The elastic modulus and Poisson’s ratio of steel were taken as 2.06 × 10 5 MPa and 0.30, respectively, and the yield strength of steel was taken as 420 MPa. The finite element mesh was generated using SOLID92 elements with a free meshing scheme. The angle steel and gusset plates were assumed to be integrally connected, and the stress distribution in the gusset plate and the connection region between the angle steel and the gusset plate was examined. The concrete foundation was not explicitly modelled; the bottom end of the lower angle steel and the bottom surface of the gusset plate were assumed to be fixed, whereas the remaining boundaries were left unrestrained. Surface loads were applied by converting the concentrated forces acting on the main and diagonal members into uniformly distributed loads on the corresponding loaded surfaces, thereby representing the load transfer of the joint under the loading conditions in the test. Bolt-hole clearance, bolt slip and contact/friction effects were not explicitly included in the model. The numerical results were therefore interpreted mainly in terms of overall stress distribution, critical stress regions and the strength reserve of the gusset plate. Predicting bolt slip, local bearing deformation or the load-deformation response in detail would require a refined contact model together with displacement measurements.

3.2 Load cases and calculation parameters

To analyse the structural behaviour of the bent angle-steel joint under design loads, the finite element model considered the stress distributions of the joint under two typical load cases, namely, tension and compression. According to the force characteristics of the main and diagonal members in practical engineering, the combined action of the loads in the main and diagonal members was considered in the finite element model to reflect the actual loading state of the joint in the concrete foundation of a transmission tower. Concentrated forces were not applied directly in the finite element model. Instead, the concentrated loads transferred from the main and diagonal members to the joint were converted into uniformly distributed surface loads and applied to the corresponding loaded surfaces. This treatment reduces artificial local stress peaks that may occur when concentrated forces are applied directly.

Table 1 lists the equivalent surface loads on each member. Under the tensile loading case, the maximum tensile force in the main member was 1488 kN, while the maximum tensile forces in the front and side diagonal members were 85 kN and 68 kN, respectively. Under the compressive loading case, the maximum compressive force in the main member was 1525 kN, and the maximum compressive forces in the front and side diagonal members were 87 kN and 70 kN, respectively. By defining these tensile and compressive loading cases, the stress distribution, location of maximum stress and strength reserve of the gusset plate under uplift tension and vertical compression were obtained, providing a basis for the subsequent analysis of finite element results and comparisons with the test results.

TABLE 1. Load parameters for specimens.

3.3 Finite element results under tension

Under tensile loading, the main and diagonal members were subjected to tensile forces. The finite element results show that the stress in the bent angle-steel joint was mainly concentrated in the connection region between the angle steel and the gusset plate. The stress contours in Figures 10, 11 show a clear load-transfer path, with regions of high stresses mainly located at the angle steel connection and at local corner regions of the gusset plate. Among the stress components, the first principal stress more clearly reflected the stress concentration of the joint under tension. The local stress distribution of the gusset plate shows that the maximum principal stress occurred at the lower-right corner of the gusset plate, where a certain degree of stress concentration existed. As this region was located within the concrete anchorage zone in practical engineering, its influence on the safety of the above-ground joint is limited. Therefore, when evaluating the safety of the joint, attention should be focused on the stress level in the above-ground joint region between the angle steel and the gusset plate. Under tensile loading, the maximum first principal stress in the connection region between the angle steel and the gusset plate was 272.6 MPa, the maximum ANSYS stress intensity was 276.8 MPa, and the maximum von Mises equivalent stress was 254.2 MPa, as listed in Table 2. These values were lower than the nominal yield stress of Q420 steel in the design check. Under the design tensile load, the gusset plate remained within the elastic range and had sufficient strength for load transfer. The critical region of the joint under tension was mainly located at the angle-steel connection and local corner regions of the gusset plate, while the stress level in the above-ground connection region remained relatively low.

TABLE 2. Critical stresses of specimens under tension.

Positive values denote tensile stress, whereas negative values denote compressive stress.

TABLE 3. Stress extrema under compression.

Positive values denote tensile stress and negative values denote compressive stress.

3.4 Finite element results under compression

Under compressive loading, both the main and diagonal members were subjected to compressive forces. The finite element results show that the bent angle-steel joint still exhibited obvious local stress concentration under compressive loading, with the region mainly located at the connection between the angle steel and the gusset plate. The third principal stress contours and the local stress distribution of the gusset plate show that the maximum compressive stress of the gusset plate was also concentrated at the corner region, as shown in Figures 12, 13. This region generally coincided with the stress concentration location under tensile loading. According to the finite element results, the absolute value of the third principal stress in the connection region between the angle steel and the gusset plate was relatively high under compression, with a minimum value of −283.5 MPa. The maximum ANSYS stress intensity was 288.0 MPa, and the maximum von Mises equivalent stress was 264.1 MPa, lower than the nominal yield stress of Q420 steel in the design check. This result indicates that, under the design compressive load, the gusset plate did not reach the yield strength and had a satisfactory strength reserve. The stress extrema under compressive loading are summarised in Table 3.

4 Comparison between test and finite element results

4.1 Comparison of stress distribution

To compare the test and finite element results, the critical strain gauges were selected according to the measured strain development. In the tension test, C12 was located on the main angle steel on Face I. When the vertical tensile load reached 800 kN, the strain measured at C12 reached 2028 με, indicating that this local region first entered the yielding stage; subsequent loading led to yielding of the double angles on Face I and tearing of the top loading plate. In the compression test, strain gauge C17 measured a strain of 1949 με when the vertical compressive load reached 1700 kN. Using the elastic relationship between strain and stress before yielding, this strain corresponded to a calculated local stress of 401.5 MPa. Therefore, the test values listed in Table 4 are not directly measured stresses, but local stresses converted from measured strains along the gauge directions. The finite element values are maximum equivalent von Mises stresses in the connection region. As the test values and finite element values represented different stress indices and directions, a strict numerical error comparison was not performed; the comparison was used to identify critical regions and assess the strength reserve of the gusset plate.

TABLE 4. Comparison of calculated local stresses and finite element results.

As shown in Table 4, the local stresses converted from the measured strains at the critical gauges under tension and compression reached or approached the yield level of the angle steel. In the finite element analysis, the maximum equivalent von Mises stresses in the connection region were lower than the nominal yield strength of 420 MPa, indicating that the gusset plate did not reach the yield condition. As the test values were local uniaxial stresses converted from strain, whereas the finite element values were equivalent von Mises stresses, the comparison was used only to identify the critical regions and assess strength safety. The test and finite element results jointly indicated that joint failure was mainly controlled by yielding or bending of the angle steel rather than by the strength of the gusset plate.

4.2 Comparison of critical regions and failure modes

The test results showed that the failure of the bent angle-steel joint under tension and compression did not occur in the gusset plate but was mainly concentrated in the angle steel and the connection region at the loaded end. Under tension, the strain gauge C12 on Face I of the angle steel yielded first, followed by the yielding of the double angles on Face I and tearing of the top loading plate, after which the joint lost its load-carrying capacity. Under compression, the angle steel on Face III bent first; as the vertical compressive load continued to increase, the bending deformation of the angle steel became more significant, and final failure occurred due to flexural yielding.

The finite element results showed that, under tension, relatively high stresses were mainly concentrated near the connection between the angle steel and the gusset plate, and the first principal stress distribution better reflected the stress concentration of the joint in tension. Under compression, relatively high compressive stresses were also concentrated near the angle steel connection, and the third principal stress distribution reflected the unfavourable stress characteristics of the joint under compression. The stress concentration regions obtained from the finite element analysis were generally consistent with the locations where the angle steel first yielded or bent in the tests, indicating that the finite element model could reasonably capture the main mechanical characteristics of the joint.

No obvious deformation or yielding of the gusset plate was observed in the tests, and the finite element analysis showed that the stress level in the gusset plate was lower than the nominal yield stress of Q420 steel in the design check. The results indicated that the failure of the bent angle-steel joint was mainly controlled by local yielding of the angle steel, compression-induced bending and the local configuration at the loading end. Tensile failure was mainly characterised by yielding of the angle steel and tearing of the loading plate, whereas compressive failure was mainly characterised by flexural yielding of the angle steel on Face III.

4.3 Load-transfer mechanism of the joint

Test data showed that the load transfer of the bent angle-steel joint can be described as follows: the load first acted on the main angle steel and was gradually transferred to the gusset plate through the bolts. Along the axis of the angle steel, the stress and strain decreased gradually from top to bottom, whereas the stress in the gusset plate increased gradually from top to bottom along the axis. This behaviour indicated that load redistribution occurred during the force transfer from the angle steel to the gusset plate. As the leg width of the gusset plate was relatively large, the stress spread outwards during load transfer, and the measured strains in the gusset plate were therefore significantly smaller than those at the strain gauges on the angle steel.

Under tensile loading, the axial stress in the angle steel increased continuously as the vertical load increased. Strain gauge C12 on Face I reached the yield strain first, followed by tearing of the top loading plate, which caused the joint to lose its load-carrying capacity. The failure process indicated that joint failure under tension was mainly controlled by the main angle steel and the local configuration at the loaded end. Under compression, as the load increased, the angle steel on Face III bent first, and strain gauges C32 and C37 yielded earlier than the other strain gauges. The deformation of the yielded region then increased gradually, and the additional load was carried by the unyielded parts on the same face, indicating obvious stress redistribution during compression. The final failure mode was flexural yielding of the angle steel on Face III. These results showed that even though local stress concentrations existed in the gusset plate, its overall stress level did not reach the nominal yield stress of Q420 steel in the design check; no obvious yielding or failure of the gusset plate was observed in the tests. These results indicated that the gusset plate of the bent angle-steel joint had a sufficient strength reserve, whereas joint failure was mainly controlled by yielding of the main angle steel, compression-induced bending or local failure at the loaded end.

5 Conclusion

The following conclusions were obtained from the full-scale tests and finite element analysis:

• The full-scale tests showed that the main damage and deformation occurred in the angle member rather than in the embedded gusset plate. In the tension test, local yielding first developed near the upper loaded end of the angle member, and the joint failed at a vertical tensile load of 1100 kN, accompanied by yielding of the double-angle member and tearing of the top loading plate. In the compression test, bending first appeared on the compressive side of the angle member, and the joint failed by flexural yielding at a vertical compressive load of 1989 kN.
• The measured strain responses indicated a clear redistribution of stress as loading progressed. Under tension, the loaded end of the angle member was the critical region as local stress concentration and eccentric force transfer developed through the bolted connection. Under compression, deformation developed mainly in the compressive angle member and the adjacent bolted region, whereas the gusset plate showed no obvious deformation or yielding. These observations indicate that practical design should pay particular attention to the loaded end of the angle member and the adjacent bolted connection.
• The finite element results showed that high stresses were mainly distributed near the connection between the angle steel and the gusset plate and at local corners of the gusset plate. The maximum von Mises equivalent stresses were 254.2 MPa under tension and 264.1 MPa under compression, which were lower than the nominal yield stress of Q420 steel used in the design check. The gusset plate still retained a strength margin under the investigated loading cases.
• Experimental tests and finite element analyses pointed to the same critical region, namely, the angle member and its loaded-end connection region. The finite element results can therefore be used to identify critical stress regions and to assess the strength reserve of the gusset plate. A refined contact model, together with displacement measurements, would be needed to predict bolt slip, local bearing deformation and the load-deformation response in detail.

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Footnotes

Edited by: Xinxin Sun, The Hong Kong Polytechnic University, Hong Kong SAR, China

Reviewed by: Xinyu Shen, Taizhou University, China

Saba Basim, University of Kufa, Iraq